Electrical power system for the CubeSTAR nanosatellite

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Electrical Power System for the

CubeSTAR Nanosatellite

by

MARTIN OREDSSON Department of Physics

THESIS for the degree of

MASTER OF SCIENCE

(Master i Elektronikk og Datateknologi)

Faculty of Mathematics and Natural Sciences

University of Oslo, September 2010

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Abstract

This thesis describes the development of an Electrical Power System (EPS) prototype for the CubeSTAR nanosatellite. Without a power system the other subsystems on the satellite cannot function, therefore a continuous and reliable power source is needed.

CubeSTAR’s triple-junction solar cells are characterized and a general introduction to spacecraft EPS is given. A solar simulator circuit that mimics the solar cell behavior is also described. The energy storage cells, which are Lithium Iron Phosphate based, are tested under various conditions. The proposed system employs two redundant and digitally controlled maximum power point trackers. To raise the efficiency of this low-voltage system, synchronous buck converters are used. A PCB implementation that fits into the pre-defined CubeSTAR structure is also presented.

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Acknowledgments

Mom and Dad, you deserve your own page, but this will have to do: thank you for your unconditional love, support, and endless supply of Swedish coffee—

they are the fundamental components of this work.

I’m very grateful to my supervisor, Associate professor Torfinn Lindem at the Electronics Group, for giving me the opportunity to work with such an interesting topic. By placing himself in the background, he has given me the freedom to explore the the topic of my thesis, and I couldn’t have asked for more.

Stein Lyng Nielsen at the Electronics Laboratory has been an invaluable resource. His willingness to share his experience on anything from printed circuit board design to the famous wine districts of Portugal has been one of the highlights the past year.

Tore Andr`e Bekkeng also deserves a special mention for being a guiding star throughout the phases of this work. Anything from L^ATEX, proofreading, Matlab to PCB design, you’ve always had the answers and the kindness to share them. I must also acknowledge the Plasma Group and especially Espen Trondsen who have given me a the best possible conditions to do my thesis work. This has included unlimited access to their electronics lab and Espen’s practical wisdom—what a privilege! My friend and fellow student Manual Lains has also been helpful in absorbing my bad jokes with minimum fuss.

Finally, my brother and aspiring mechanical engineering wizard, Mattias;

thanks man.

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List of Figures

1.1 CubeSTAR 3D Model . . . 2

1.2 CubeSTAR Subsystems Overview . . . 3

2.1 ASTM standard solar spectrum . . . 6

2.2 Front and rear view of a Spectrolab solar cell . . . 9

2.3 Energy bandgap between valence- and conduction bands . . . 10

2.4 Triple junction solar cell stack-up . . . 11

2.5 Triple junction solar cell equivalent circuit . . . 12

2.6 Triple junction solar cell IV plot . . . 14

2.7 The effect of varying irradiance levels on the I-V curve. . . 15

2.8 The effect of varying temperature on the I-V curve. . . 16

2.9 Dual plot of I-V and P-V curve . . . 17

2.10 The effect of internal resistance on the I-V curve. . . 19

2.11 The effect of internal leakage resistance on the I-V curve. . . . 20

2.12 Constant power load lines intersecting the IV curve . . . 21

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2.13 Solar incident angle: Kelly cosine vs Cosine law . . . 23

2.14 Geometry used to calculate average orbital power . . . 26

2.15 Contour plot of the angular response . . . 27

3.1 EPS main functional parts overview . . . 30

3.2 Direct Energy Transfer system block diagram . . . 31

3.3 Peak Power Tracking system block diagram . . . 32

3.4 LEO reference view . . . 33

3.5 Geometry to calculate orbital eclipse and sunlit periods . . . . 34

3.6 Low-earth orbit temperature profile . . . 36

3.7 MPPT control block diagram . . . 37

3.8 MPPT: Perturb and Observe flow diagram . . . 40

3.9 Dimensions and picture of LiFePO4 cell . . . 41

3.10 LiFePO₄ cycle life performance . . . 42

3.11 Total solar array energy requirements . . . 43

3.12 CubeSTAR batterypack open-view . . . 47

3.13 LiFePO₄ charging regime . . . 48

3.14 Equivalent circuit during the constant voltage charging phase. 49 3.15 Component heat removal in space/terrestrial conditions . . . . 52

4.1 System overview . . . 56

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4.2 Solar array configuration . . . 57

4.3 Synchronous buck converter . . . 58

4.4 Buck converter dutycycle vs V_out . . . 59

4.5 Buck converter ON/OFF states . . . 60

4.6 Oscilloscope view of the switch node voltage . . . 61

4.7 Deadtime insertion on the gate driver signals . . . 62

4.8 Buck inductor voltage and current waveforms . . . 63

4.9 System state machine . . . 67

4.10 MPPT operation modes . . . 69

4.11 PID operation mode . . . 70

4.12 Transducer interface design (TID) block diagram. . . 71

4.13 Implemented TWI slave flow diagram . . . 76

4.14 Microcontroller power scheme . . . 77

4.15 Device: TPS2556 from TI . . . 79

4.16 Device: INA138 from TI . . . 80

4.17 Fault protection and monitoring unit . . . 81

5.1 The first PCB prototype . . . 83

5.2 The second PCB prototype . . . 84

5.3 The third PCB prototype . . . 85

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5.4 Four layer PCB stackup . . . 86

5.5 The CubeSTAR module and backpanel templates . . . 87

5.6 Trace inductance and plane capacitance geometries. . . 89

5.7 Trace resistance vs width . . . 90

5.8 Trace loop inductance vs width . . . 91

5.9 Typical noise path . . . 92

5.10 Return current loop frequency dependency . . . 94

5.11 Transients with and without decoupling . . . 96

5.12 PCB measures taken to reduced noise . . . 97

5.13 Avoiding the gaps in the ground plane . . . 98

5.14 A simplified parasitic model for the switch node. . . 99

5.15 SR parasitic SPICE model . . . 101

5.16 Parasitic turn-on simulation . . . 102

5.17 Capacitive coupling on the SR gate . . . 103

5.18 Ringing sans snubber . . . 105

5.19 New ringing frequency with capacitor . . . 106

5.20 Damping the ringing with a RC snubber . . . 107

6.1 UTJ diode dark-current test setup . . . 110

6.2 Test: Dark current measurement in -20^◦C. . . 110

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6.3 Test: Dark current measurement in 3^◦C. . . 111

6.4 Test: Dark current measurement in 23^◦C. . . 111

6.5 Extrapolation of non-linear regression fits . . . 112

6.6 Comparison of V_oc and extrapolated dark-current values . . . 113

6.7 Test: Angular response of two series connect UTJ solar cells. . 114

6.8 Solar simulator IV curve on which the MPPT testing was done.115 6.9 Test: The effect of dutycycle on current, voltage and power. . 116

6.10 Test: P&O characteristic oscillation . . . 117

6.11 Test: Systen response to varying Voc . . . 118

6.12 Test: System state transition . . . 119

6.13 Test: Charge-discharge-charge cycling . . . 120

6.14 Test setup to test the large signal response. . . 121

6.15 Battery charging in MPPT mode with dummy load . . . 121

6.16 Dummy load draw on battery charging in PID mode . . . 122

6.17 LiFePO4 over-discharge abuse test . . . 123

6.18 Setup for the -17 degree LiFePO₄ discharge test. . . 124

6.19 Test: LiFePO₄ cold discharge characteristics . . . 125

6.20 Test: LiFePO4 vs Lithium Ion Polymer discharge . . . 126

A.1 Solar simulator IV curve . . . 135

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A.2 Solar simulator IV and PV curves . . . 136

A.3 Circuit diagram of the solar cell simulation model. . . 137

A.4 Solar simulator PCB layout . . . 138

A.5 Solar simulator photograph . . . 139

A.6 Solar simulator V_oc and I_sc range . . . 140

B.1 SPICE circuit used to generate the plots in this section. . . 144

C.1 PID to Buck block diagram . . . 149

C.2 PID regulator block diagram. . . 150

D.1 Start and stop conditions. . . 154

D.2 The first byte after the start condition. . . 155

D.3 Acknowledge on the TWI bus. . . 155

D.4 Master read (top) and write (bottom) transaction. . . 156

E.1 TopSilk Layer . . . 178

E.2 TopStop Layer . . . 179

E.3 TopPaste Layer . . . 180

E.4 TopElec Layer . . . 181

E.5 Ground Layer . . . 182

E.6 Power Layer . . . 183

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E.7 BotElec Layer . . . 184 E.8 BotStop Layer . . . 185 E.9 Drill file . . . 186

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List of Tables

2.1 Key parameters from the UTJ datasheet . . . 8 2.2 Required energy to ionize different semiconductor materials . . 10 2.3 Solar array power output summary . . . 28

3.1 Lithium Iron Phosphate batteries from A123 Systems . . . 43 3.2 Battery capacity calculations summary. . . 46

4.1 Theoretical buck converter parameters. . . 66 4.2 Telemetry data sent on master request. . . 75 A.1 Spectrolab UTJ Characteristics . . . 134 A.2 Solar cell simulation circuit parameters . . . 139

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Chapter 1 Introduction

This thesis gives a theoretical introduction to spacecraft electrical power systems (EPS) and describes the design and development of a prototype EPS for the CubeSTAR nanosatellite. Providing power for electronics that operate in space give rise to a unique set of constraints, and as the only available source of power, the EPS is literally the lifeline of the other systems on the satellite.

By using a single switching regulator with a digital control loop, the maximum amount of solar power can be converted to electrical energy. At the same time, the system controls charging of the energy storage cells that are vital during the solar eclipse periods. Thus, a low parts-count and efficient system is made possible.

1.1 Background and Motivation

This thesis is a part of the CubeSTAR student satellite project at the Uni- versity of Oslo (UiO). The project is a part of the Norwegian student satellite program (ANSAT) which is mainly funded by the government agency Norwegian Space Centre (NSC). The ANSAT program itself is run by the Norwegian Center for Space-related Education (NAROM) which is based at Andøya Rocket Range (ARR). The scientific mission of CubeSTAR is to demonstrate a new concept of measuring the electron density in the iono-

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Figure 1.1: The CubeSTAR satellite has dimensions 20cm ×10 cm × 10cm and are covered by solar cells on four sides. The four probes for measuring electron density can be seen on the right side of the structure, while the communication antennas are shown to the left.

spheric plasma, with a new multi-probe system that promises greater spatial resolution than its predecessors. But in addition to that, the CubeSTAR mission has an educational component which is to provide a platform where students from several disciplines can work together towards a common goal of launching their work into space.

1.2 CubeSTAR and the Cubesat Standard

The Cubesat standard, developed by California Polytechnic State University and Standford University in 1999, is a specification of a type of miniaturized satellite with the dimensions of a 10 cm cube and a maximum weight of one kilogram. This is known as a ”1U” satellite. It didn’t take long though before scaled versions of this 1U structure showed up, and both ”2U” (20cm × 10

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cm × 10cm) and ”3U” (30cm × 10cm × 10cm) structures have been built and launched. The CubeSTAR satellite is built after the 2U specification.

ADCS COMM OBDH EPS PAYLOAD

CubeSTAR satellite

Figure 1.2: The Electrical Power System (EPS) is one of the five CubeSTAR subsystems.

The satellite naturally divides itself into subsystems, which form the basis for separate work groups where each group works on a single subsystem.

These range from Attitude Control (ADCS) to stabilize the satellite, communication link (COMM), on-board data handling (OBDH), electrical power system (EPS) and the scientific payload as mentioned. Communication with the satellite is made possible by ground stations at UiO and ARS/Andøya among others.

1.3 Goals of Present Work

The goals of this work have been to provide answers to the following questions:

• How much energy is available to the satellite and how can this energy be utilized most efficiently?

• How should the energy be stored on-board?

• How is the electrical energy distributed to the other subsystems?

• How can the answers to the above questions be implemented on a printed circuit board that is within the physical constraints of the 2U formfactor?

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In addition, to gap part of the bridge of discontinuity that often plagues Cubesat projects, an attempt has been made to generate and present information in such a way that it could be picked up by the next wave of students.

1.4 Thesis Outline

The explanatory approach taken here is to follow the flow of energy through the system, from the Sun, through the regulation system and via the batteries, before ending up at the subsystems.

In Chapter 2, the Sun’s role as the ultimate energy source is briefly described, before moving on to the semiconductor devices that convert solar energy to electrical energy on most of CubeSTAR’s surface; the solar cells. Having gotten the energy aboard, Chapter 3 describes the EPS itself: the maximum power point tracking, the Lithium Iron Phosphate batteries, and system reliability are keywords here.

Arriving at Chapter 4, the background information from the previous chap- ters is now crystalized into a system design which is described here, but also spills into Chapter 5 which deals with the actual printed circuit board design.

The testing that have been done on various parts of the system is presented in Chapter 6, while Chapter 7 concludes the thesis with a few words on what this all means and how it can be used by future CubeSTAR worker bees.

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Chapter 2 Harvesting Energy from the Sun

The CubeSTAR satellite will harvest energy from the Sun through the use of solar cells. This chapter deals with the theoretical background for the conversion from solar- to electrical energy in the context of the chosen triple- junction solar cells.

2.1 Solar Energy

To evaluate the amount of available solar energy for a spacecraft, the spectral irradiance of the Sun at the Earth’s mean distance, or one astronomical unit (1AU), is often used. Referring to the lack of attenuation in the vacuum conditions above the Earth’s atmosphere, this spectrum is known as the Air Mass Zero spectrum, or AM0 for short.

While the atmosphere absorbs certain wavelengths under terrestrial conditions, the solar spectrum in space closely matches a black-body radiator at 5780K. These similarities are illustrated in Figure 2.1 where the Air Mass Zero (AM0) reference¹ spectrum is plotted together with the AM1.5 (terrestrial conditions) and 5780K black-body plots. The peak of the spectrum,

1The data for the reference spectrum (ASTM E-490) can be found here:

http://rredc.nrel.gov/solar/spectra/am0/

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0 500 1000 1500 2000 2500 0

0.5 1 1.5 2

Wavelength (nm) Spectral Irradiance (Wm−2 nm−1 )

5780K Black Body

Extraterrestrial Spectrum (AM0) Terrestrial Spectrum (AM1.5)

Figure 2.1: While the terrestrial solar spectrum suffers from absorption of various wavelengths in the atmosphere, the conditions in space closely matches those of a black body radiator.

which coincidentally is the part our eyes evolved to see, is at wavelengths from 400 to 700 nanometers.

The photon energy E, in units of electron volts (eV), is

E = hc

λ (2.1)

whereh= 4.135×10⁻¹⁵eV·s is the Planck constant, c= 2.998×10⁸ m/s is the speed of light in vacuum, and λ is the photon wavelength in meters. As Figure 2.1 shows, at shorter wavelengths (i.e., higher energies) the photon density drops off abruptly, and the Sun emits very little electromagnetic radiation below wavelengths of about 300 nm. In other words, almost no photons carry an energy greater than

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E_max≈ 1240·eV nm

300 nm ≈4 eV

A more practical quantification of the incoming solar energy can be found by integrating the energy under the AM0 curve in Figure 2.1. The result is known as the solar constant and is a measure of flux, i.e. the amount of incoming electromagnetic radiation per unit area that would be incident on a plane perpendicular to the rays. Ignoring the small (less than 7%) annual variations due to Earth’s varying distance to the Sun, the solar constant has been measured to be roughly 1366 Watts per square meter, or 136.6 mW/cm².

2.2 From Solar- to Electrical Energy

An incoming solar energy of 1366 watts per square meter would not be of much use without a way to convert it to electrical energy. This job is typically done with solar cells. Although the photovoltaic effect was first recognized by French physicist A. E. Becquerel in the year 1839, it wasn’t until 1883 that the first solar cell was built by Charles Fritts. His new invention was capable of transforming 1% of the incoming solar energy to electrical energy.

Fast forward 130 years, and luckily, CubeSTAR is mounted with solar cells that convert solar energy to electrical energy with an efficiency of around 28%. The chosen cells for CubeSTAR are Spectrolab’s Ultra Triple Junction (UTJ) solar cells, shown in Figure 2.2. For easy reference the most important parameters from the UTJ datasheet are re-hashed in Table 2.1. The meaning and significance of these parameters are explained in Section 2.4.

The cells are delivered in an assembly of solar cell, interconnects and cov- erglass, known as a CIC, and are approximately 160 microns thick with an area[3] of 26.62 cm². The rear side is mounted with a silicon bypass diode that sits anti-parallel relative to the solar cell’s anode-to-cathode direction.

The role of the bypass diode is to prevent a partially shadowed or damaged individual CIC in a series string from being forced into reverse bias.

When sunlight hits these solar cells, one of three things happens:

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Table 2.1: Key parameters from the UTJ datasheet, AM0, 28^◦ Parameter Value Description

J_sc 17.05 mA/cm² Short-circuit current density J_mp 16.30 mA/cm² Current density at the MPP V_oc 2.665 V Open-circuit voltage

V_mp 2.350 V Voltage at the MPP

Cff 0.84 Fill factor

η 28.3% Efficiency

jsc 5 µA/cm²/^◦C Temperature coefficient for Jsc

jmp 1 µA/cm²/^◦C Temperature coefficient for Jmp

voc -5.9 mV/^◦C Temperature coefficient for Voc

vmp -6.5 mV/^◦C Temperature coefficient for Vmp

1. The photon passes straight through the material.

2. The photon is reflected off the surface.

3. The photon is absorbed in the semiconductor material.

Reflection is related to unfavorable incident angles and surface coating of the cells, and will not be dealt with here. To understand why the solar cell might be transparent to certain photons while absorbing others, a short de-tour into the basic workings of semiconductors is necessary.

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Figure 2.2: Front and rear sides of a CIC from Spectrolab showing the cathode interconnects (A,B,C), the anode (D) of the monolithic bypass diode, the parallel electrodes (E) that terminate at the cathodes, the cell’s anode (G), and the integral monolithic bypass diode (F) which protects the cell in the case of reverse bias.

2.3 Semiconductor Basics

In an isolated atomic structure there are discrete energy levels associated with each orbiting electron. When two atoms form a molecule, their atomic orbitals combine and produce a number of molecular orbitals. As the number of atoms increase to form solids, the number of molecular energy levels (orbitals) increase to the point where it is natural to speak of continuous bands of energy instead of discrete energy levels. This electronic band structure, which is due to diffraction of the quantum mechanical electron waves in the periodic crystal lattice, is the underlying determinant of a material’s electrical properties.

There are two bands of special interest to us. The valence band which is the highest occupied band, and the conduction band which is the lowest unoccupied band. The energy gap, E_g, between these two bands is known as the material’s band gap. Suffice for our discussion, it is a measure of the amount of energy required to free an outer shell electron from its orbit around the nucleus to a free (conducting) state.

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Energy gap = Eg

Photon

Electron Conduction Band

Valence Band

Figure 2.3: The photon energy must be greater or equal to the bandgap in order to free an electron from the valence band and make it a mobile charge carrier.

In fact, a semiconductor is (arbitrary)defined as a material with 0<Eg <3 eV at a temperature of 300K, while insulators and conductors are defined as materials with E_g > 3 eV and E_g = 0 respectively. The voltage across a semiconductor and the band gap energyEg are closely related through [9, p.

11]

V_D ≈ E_g

q −0.4V

where we have divided by the elementary charge q in order to get the right units. Table 2.2 lists the band gap energies[9, 20] of a few well-known semiconductor materials².

Table 2.2: Required energy to ionize different semiconductor materials.

Semiconductor Material Bandgap E_g Voltage V_D

Silicon (Si) 1.1 eV 0.7V

Germanium (Ge) 0.67 eV 0.27V

Gallium Arsenide (GaAs) 1.41 eV 1.01V

Gallium Indium Phosphide (GaInP2) 1.85 eV 1.45V

Triple junction solar cells are, simply put, constructed by stacking three

2At a temperature of T = 300K

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different semiconductor materials on top of each other. If a photon has insufficient energy to knock loose an electron in a layer, it will simply pass through to the next layer. In the cells from Spectrolab, the top GaInP₂ layer is transparent to all but the most energetic photons in the ultraviolet and visible part of the spectrum. The second GaAs layer absorbs near-infrared

GaInP₂ GaAs

Ge Eg1

Eg2 > Eg1

Eg3 > Eg2 > Eg1

Figure 2.4: The collective ability of triple junction solar cells to absorb light of different wavelengths is the main reason for their superior efficiency compared to conventional solar cells.

light while the bottom Ge layer absorbs all the lower photon energies in the infrared that are above 0.67 eV. By combining semiconductor materials with different bandgap energies this way, higher conversion efficiencies are possible due to the stack’s collective ability to match the solar spectrum.

When a layerdoes absorb photons, the solar energy excites electrons into the material’s conduction band where it is free to sign up to do work as electrical current. How this photo-generated current and voltage behaves electronically is the topic for the next section.

2.4 Electronic Behavior of a Triple Junction Solar Cell

To understand the electronic behavior of the triple junction solar cells, the equivalent³ circuit in Figure 2.5 is used. Although the use of three diodes

3The monolithic bypass diode is not included, as it does not affect normal operation.

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give a better feel for the higher output voltage of triple junction cells, its use here is more illustrative than practical, as it unnecessarily clutters the equa- tions without the benefit of increased information output from the model.

Therefore in the following the diode string will be treated as a single diode.

All plots in this section were created with the SPICE model from Appendix B. Although the model ignores more exotic effects such as the parallel non- ohmic current paths caused by recombination (which requires a second parallel diode in the model), it was constructed in such a way as to match the output characteristics of Spectrolab’s cells as closely as possible.

R^SH R^S

D^GaAs D^GaInP₂

D^Ge

I^D I^SH I

V^OC V^D

+ I^SC

Figure 2.5: An equivalent circuit of a triple junction solar cell. The monolithic bypass diode (not shown) has its anode connected to the negative terminal and its cathode to V_D.

With the simplifications made, the cell acts as a constant current source shunted by a diode. The internal resistance to the current flow, represented by a lumped resistorR_S, is primarily caused by the resistivity of the semiconductor material, but also from the metal grid and contacts on the cell. The other (shunt) resistorR_SH represents the leakage current across the junction, and for a high-quality cell we have that R_SH >> R_S.

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2.4.1 Short-Circuit Current

From Kirchoff’s Current Law it’s clear that the output current I from the cell is

I =Isc−(ID+ISH)

where the photo-generated current I_sc is proportional to the illumination, I_SH = V_D/R_SH is the current through the shunt resistor, while the current ID through an isolated photocell is given by the Shockley diode equation;

I_D =I₀

· exp

µ qV_D nk_BT

¶

−1

¸

where q is the elementary charge, V_D is the voltage across the diode(s), k_B is the Boltzmann’s constant, T is the absolute temperature, n = 1 is the ideality factor for an ideal diode, and finally the temperature- and area (A) dependent reverse saturation current

I₀ ∝A·exp µ

− E_g kBT

¶

(2.2)

The output current then becomes

I =I_sc−I₀

· exp

µ qV_D nk_BT

¶

−1

¸

− V_D

R_SH (2.3)

where the ground leakage current represented by the last term is negligible compared toIsc and ID.

If the output is shorted, the output voltage is trivially zero, which means that the short-circuit current is the same quantity as the photo-generated current, and thus a measure of the irradiance level, as shown in Figure 2.7.

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0.0V 0.5V 1.0V 1.5V 2.0V 2.5V 3.0V 0mA

100mA 200mA 300mA 400mA

500mA I(Vbias)

Isc

Voc

--- D:\_Work_dir\LTSpice_wrk\Closing In\UTJ_sim.cir ---

Figure 2.6: The simulated characteristic IV curve of a single triple junction solar cell, plotted here with AM0 conditions in room temperature with Rs = 50mΩ and Rsh = 300Ω.

2.4.2 Open-Circuit Voltage

The cell’s open-circuit output voltage V_OC is the voltage, V_D, across the current source less the small drop over R_S, or

V_D =V_OC +IR_S

In the open-circuit condition, there can be no current flow, I =I_oc= 0 and thus

Ioc=Isc−I0

· exp

µqV_oc nkT

¶

−1

¸

− V_oc R_SH = 0 Ignoring the last term and solving for V_oc gives

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0.0V 0.4V 0.8V 1.2V 1.6V 2.0V 2.4V 2.8V 0mA

100mA 200mA 300mA 400mA

500mA I(Vbias)

1 W/m^2 500 W/m^2 1000 W/m^2 1366 W/m^2

Figure 2.7: The effect of varying irradiance levels on the I-V curve.

V_oc=V_T ·ln µ

1 + I_sc I0

¶

≈V_T ·ln µI_sc

I0

¶

(2.4)

where V_T =k_BT /q is the thermal voltage. From Equation 2.2 we have that I₀ is proportional to exp(−E_g/k_BT), so

V_oc≈V_T ·ln µI_sc

I₀

¶

≈ k_BT q

µ

lnI_sc− E_g k_BT

¶

∝T (2.5)

which shows that the net effect is that Voc increases linearly with increasing temperature. In Figure 2.8, parameters within the SPICE model was ad- justed to match the negative temperature coefficient from the datasheet, and as such, the curves represent the theoretical response to varying temperature.

Equation 2.4 also explains why the change in open-circuit voltage was so small relative to the change inI_scunder the varying irradiance conditions in Figure 2.7; V_oc depends logarithmically on the I_sc/I₀ ratio which in turn depends linearly on the irradiance, as we saw earlier. Replacing the current with the current density expression above will also reveal that V_oc is independent of the cell area.

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0.0V 0.5V 1.0V 1.5V 2.0V 2.5V 3.0V 3.5V 0mA

100mA 200mA 300mA 400mA

500mA I(Vbias)

28°C

- 22°C

- 74 °C 78°C

Figure 2.8: The open-circuit voltage is a strong function of temperature, while the temperature’s effect on the short-circuit current is small enough to be ignored in this model. The temperature values are retro-fitted values from the datasheet.

2.4.3 Maximum Power Point

Every point on the I-V curve has a power associated with it, given by

P =V I =V

·

I_L−I₀ µ

exp µV

VT

¶

−1

¶¸

(2.6)

In order to generate power, both V and I must be non-zero, so V 6= V_oc and I 6= I_sc, and thus the cell must be operated between these two points on the I-V curve.

The maximum power point (MPP) of a solar cell is the operating point on the I-V curve where the product of the delivered output current, I_L, and the voltage across the cell, V, is at its maximum. We shall call this point

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0.0V 0.3V 0.6V 0.9V 1.2V 1.5V 1.8V 2.1V 2.4V 2.7V 3.0V 0mA

100mA 200mA 300mA 400mA 500mA 0.00W 0.25W 0.50W 0.75W 1.00W 1.25W

I(Vbias)

Vmp Imp

MPP I(Vbias)*V(31)

Pmax

Figure 2.9: Every point on the I-V (bottom) curve has a corresponding point on the P-V (top) curve. To extract maximum power from the cell, it must be operated at the MPP.

P_max =V_mpI_mp

and take it to be the point where the maximum power is generated, as can be seen in Figure 2.9.

Plugging the pair of Vmp and Imp into Equation 2.3 we find that the current at the MPP is,

I_mp=I_L−I₀

· exp

µV_mp VT

¶

−1

¸

(2.7)

From Figure 2.9 it is clear that the power derivative with respect to voltage must be zero at the MPP (where V = V_mp and I = I_mp), so

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dP

dV = IL−I0

· exp

µV_mp V_T

¶

−1

¸

− V_mp

V_T I0·exp µV_mp

V_T

¶

= I_mp− V_mp

V_T I₀·exp µV_mp

V_T

¶

= 0 (2.8)

Using the result from Equation 2.8 together with Equation 2.4 we find that the voltage at the MPP is

V_mp = I_mpV_T I₀ exp

µV_mp V_T

¶

= I_LV_T −I₀V_T · h

exp

³Vmp

VT

´

−1 i I₀·exp

³Vmp

VT

´

= I_LV_T I0·exp

³Vmp

VT

´+ V_T exp

³Vmp

VT

´ −V_T

= V_T ·exp µ

−Vmp

V_T

¶ µIL

I₀ + 1

¶

−V_T (2.9)

Equation 2.9 is a so-called transcendent equation whose solution is usually found by graphical or numerical methods. We will not pursue such matters here, and simply state the first of two alternative solutions given by [7, eqn.

3.13—3.15], which is

V_mp =V_oc−3V_T (2.10)

We’ll let the power-discussion rest for now, and run through the rest of the datasheet parameters, before picking up the power again in Section 3.4, where the focus will be on how to actually maximize the output power and do something useful with it.

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2.4.4 Fill Factor

We will now define thefill factor (FF) as the ratio between the actual power output P_max, and the product of open-circuit voltage V_oc and short-circuit current I_sc.

F F = V_mpI_mp

V_ocI_sc (2.11)

The fill factor is a measure of a cell’s energy conversion efficiency, and as seen from Figures 2.10 and 2.11, the ratio is strongly dependent on the shunt- and series resistance in the cell.

0.0V 0.3V 0.6V 0.9V 1.2V 1.5V 1.8V 2.1V 2.4V 2.7V 3.0V 0mA

100mA 200mA 300mA 400mA

500mA I(Vbias)

0.5ΩΩΩΩ 1ΩΩΩΩ 2ΩΩΩΩ

0.001ΩΩΩΩ

Figure 2.10: The effects of an increasing series resistance (R_S). High quality cells have low series resistance.

As an example of their impact, we can consider the case of a decrease in shunt resistance in Figure 2.11. For every new lower value of RSH, the product of I_mp and V_mp decreases, while V_oc and I_sc remain constant, with a lower fill factor as a result.

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0.0V 0.3V 0.6V 0.9V 1.2V 1.5V 1.8V 2.1V 2.4V 2.7V 3.0V 0mA

100mA 200mA 300mA 400mA

500mA I(Vbias)

15ΩΩΩΩ 25ΩΩΩΩ

50ΩΩΩΩ 1000ΩΩΩΩ

Figure 2.11: The effects of a decreasing shunt resistance (R_SH). High quality cells have high shunt resistance.

2.4.5 Efficiency

Lastly, there is the power conversion efficiency, which is a measure of the cell’s ability to convert solar energy into electrical energy. Being the ratio of output- to input power, it is dimensionless and given by

η= P_m Pin

= V_mp·I_mp

A·G =F FV_oc·I_sc Pin

=F FV_oc·I_sc

A·G (2.12)

whereG= 1366 W/m² is the solar constant and A= 26.6 cm² is the area of a single UTJ cell from Spectrolab. Note that the cell efficiency is referenced to AM0 conditions

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2.4.6 Loading the Solar Cell

When a load is directly connected to a non-linear source such as the solar cell, the system’s operating point is at the intersection of IV curve and the load line. For a simple linear load with constant resistance, the load line would be a straight line through origo, which, in the general case, would not intersect the IV curve at the MPP but rather at some arbitrary point on the IV curve.

In Figure 2.12, another type of load line can be seen; aconstant power load.

Among the type of loads that are characterized by such a load line, is the switching regulator⁴, which aims to regulate its output at a steady voltage regardless of variations in input voltage or load current draw.

Figure 2.12: Constant power load lines (P₁ and P₂) intersect the IV curve in two places. Only B2 is stable, and this is where the system naturally operates. Figure reproduced from [19].

If the power is P =V I and the operating point moves away from this point,

4For example, if the solar cell voltage increases, the control loop of the regulator would reduce its dutycycle, which in turn would reduce the input current of the regulator. There- for, an increase in the input voltage (i.e., solar cell output voltage) results into a current decrease, and vice versa, making the switching regulator look like a constant power load to the solar cell.

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to

P + ∆P = (V + ∆V)(I+ ∆I) (2.13)

then, by ignoring the small term, the change can be expressed as

∆P = ∆V I+ ∆IV (2.14)

At the maximum power point, ∆P should necessarily be zero and lie on a lo- cally flat neighborhood, so the relationship in the limit between the dynamic and static impedance at the maximum power point, can be stated as

∆V

∆I =−V

I (2.15)

When the solar cell is operated away from P_max, it has been shown in [10]

that only point B₂ in Figure 2.12 is stable and any perturbation from it will generate a restoring power in the direction of Voc to take the operation back to B₂. In other words, electrically stable operation of the solar array is characterized by

·dP dV

¸

load

>

·dP dV

¸

source

(2.16)

2.5 Angular Response of a Solar Cell

A fundamental parameter in all solar array analysis is the angle (η) between the solar panel normal vector (Nb) and the spacecraft-Sun vector (S). Inb general, the cosine of the angle between the two vectors is given by the the sum of their direction cosines. Thus, by using elementary vector identities the angle for any combination of panel normal and Sun vector can be calculated with Nb •Sb=~n_x~s_x+~n_y~s_y+~n_z~s_z = cosη (2.17)

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This is an important result, because the amount of solar generated current from a cell is proportional to the cosine of the angle between the two vectors—

or, at least up until a certain point. Beyond 50^◦, increased reflection causes the angular response to deviate from the cosine law, and the actual response is more accurately expressed by what is known as the Kelly cosine:

ρ=−0.369 cos³θ+ 0.637 cos²θ+ 0.750 cosθ−0.015

where θ is the angle between the Sun vector and the solar panel normal.

0 10 20 30 40 50 60 70 80 90

0 0.2 0.4 0.6 0.8 1

Normalized Current

Incident angle (θ in degrees)

Cos θ Kelly cosine

Figure 2.13: Output current from a solar cell is proportional to the cosine of the incident angle—up to about 50^◦ at which point the Kelly cosine is more accurate. No current is produced at angles > 85^◦.

As seen in Figure 2.13, the actual electrical output drops off slightly steeper than what the cosine function predicts, and no current is produced at angles greater than 85^◦. However, the deviation is not large enough to outweigh the benefits of simpler calculations, so the Kelly cosine is therefore rejected here in favor of the cosine function.

The input solar energy, I, on a spacecraft surface is given by

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I =A·K·cosη (2.18) where A is the area in m², K is the solar constant (1367 W/m²), and ηis the angle between the surface normal and Sun vector. With Equation 2.18 and Figure 1.1 in mind, four different cases will be considered where an attempt is made to illuminate how the spacecraft’s position will affect the effective area A·cosη and thus the power output from the cells.

2.5.1 Case 1: Minimum Sun

This case is trivial since if one of the two sides without mounted solar cells have their normal vector aligned with the Sun vector, the effective solar cell covered area is zero and no power is produced.

A_min = 0

2.5.2 Case 2: One side facing the Sun

If the normal vector of a surface with four mounted solar cells is aligned with the Sun vector the effective area is

A_one= 4×26.6cm²×cos 0 = 106.5cm² and the produced power is

P_one = 1367W/m²×0.0106.5m²×28% = 4.08W (2.19)

2.5.3 Case 3: Maximum Sun

The maximum possible effective area is when two sides with mounted cells simultaneously face the Sun such that their individual projected area in the direction of the Sun equals the cosine of the angle. The total area is

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A_max= 2×4×26.6cm²×cos 45 = 150.6cm² and the produced power is

P_max = 1367W/m²×0.01506m²×28% = 5.76W (2.20)

2.5.4 Case 4: Average effective area for a free-tumbling spacecraft

By letting the Sun vector lie along one of the axis, the projected area in each dimension is sufficiently expressed by the spherical coordinates for the normal vector:

N_x = sinβcosα N_y = sinβsinα Nz = cosβ

Negative values of the cosine function are discarded since a surface is only illuminated for angles between 0^◦ and 90^◦. The total projected area in the direction of the Sun,A_tot, is found by integrating the contributions from each face over the 90^◦ rotation about two axis, or

A_tot =

π

Z2

0

π

Z2

0

(A₁sinβ·cosα+A₂sinβ·sinα+A₃cosβ)dβ·dα where A_1,2,3 represent the areas of each of the three sides that at any given time can face the Sun.

In terms of actual solar cell area, the solar panel configuration from Figure X means one of the three areas will be zero. This fact is taken into account by letting the empty face be represented by A_1,2,3 in succession and averaging the result over the three trials. But that is equivalent to replacing each

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X

Figure 2.14: Solar panel normal vector and geometry used to estimate the output power for a free tumbling spacecraft.

individual side’s area with the average area (i.e., two thirds of the area of one side) of the three exposed sides, or

A=A_1,2,3 = 4 cells×26.6 cm²× 2

3 = 70.9 cm² = 0.00709 m² so the numerical value for the total area becomes

A_tot =A·

π

Z2

0

π

Z2

0

(sinβ·sinα+ sinβ·cosα+ cosβ)dβ·dα=A·(2 + π 2)

To get a feel for the angular response ofA_tot/A, the a Matlab script was used to sum⁵ up the contributions and average them over the summation limits.

It should be noted however, that Figure 2.15 does not illustrate the actual angular response of the spacecraft, but rather that of the equivalent scenario with scaled average sized solar cells on all sides.

5The integrals were approximated with sums.

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0 10 20 30 40 50 60 70 80 90 0

10 20 30 40 50 60 70 80 90

Angle α (degrees)

Angle β (degrees)

Figure 2.15: Angular response when all sides are covered by imaginary averaged sized solar cells.

The averaged projected area A_avg in the direction of the Sun is then found by dividing Atot with the integration limits, or

1

A_avg = 1 A_tot ·

π

Z2

0

π

Z2

0

dβ·dα ⇒ A_avg = A_tot

π²/4 (2.21)

Thus, the numerical average projected area in the direction of the Sun for a free tumbling spacecraft is

A_avg =A·2 + ^π₂

π²/4 = 0.0071 m²· 8 + 2π

π² = 0.01026 m² (2.22)

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Finally then, the estimated average input power during the sunlit portion of the orbit is

P_avg = 1367W/m²×0.01026m²×28% = 3.93W (2.23) for solar cells with 28% efficiency in AM0 conditions.

The four cases considered in this section are summarized in Table 2.3.

Table 2.3: Effective area and produced power under various spacecraft posi- tions.

Case Area Power

1: Minimum area 0 0 W

2: One side only 106.5 cm² 4.08 W 3: Maximum area 150.6 cm² 5.76 W 4: Average area 102.6 cm² 3.93 W

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Chapter 3 Spacecraft Electrical Power Systems

3.1 Objectives

The main objective of the electrical power system (EPS) is to provide the other subsystems with a reliable and continuous power source. Typical building blocks of such a system consists of a solar array, energy storage batteries and power processing electronics, which perform:

1. Conversion from solar energy to electrical power 2. Energy storage in electrochemical cells

3. Control and regulation of the spacecraft’s electrical power 4. Power distribution to other loads

Having already dealt with the solar array in Chapter 2, the main focus here will be on the second and third points, while the fourth task will be simplified by choosing batteries with an operating voltage that lies in the range of what many of the subsystems are expected to operate within. Thus, in the current setup, a de-centralized distribution scheme is used.

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Electrical Power Subsystem

Power Regulation &

Control Power

Source Power

Distribution Energy

Storage

Figure 3.1: Functional overview of the EPS. A de-centralized distribution approach is proposed, where post-regulation is performed at the individual sub-system level if necessary.

3.2 Power Regulation Topology

Electrical power systems used for spacecrafts in LEO can broadly be divided into two types; the Direct Energy Transfer (DET) approach and the Peak Power Transfer (PPT) approach. All other configurations are variations, derivations or combinations of these two basic types.

Since they both have common building blocks in the form of solar arrays and power distribution units, the distinction between DET and PPT lies in how the power processing electronics conditions the solar array and storage batteries. While a PPT system aims to extract the maximum power from the solar array and hence dissipate very little power internally, a DET system employs a shunt regulator to dissipate any excessive power.

In the following sections, a brief introduction to DET systems will be given before moving on to the PPT systems which will be the main focus. Al- though both types allow for a regulated or unregulated power bus, only the unregulated types will be evaluated here since a de-centralized regulation approach has been chosen. There is no need to regulate the main bus, as the subsystems themselves will regulate their own supply.

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3.2.1 Direct Energy Transfer (DET)

In the DET approach, the power from the solar array is directly transferred to the loads (via the distribution unit). To regulate the bus voltage at a predetermined level, a shunt regulator dissipates any excessive power as heat within the system which may require large heatsinks.

SOLAR ARRAY

POWER DISTRIBUTION

UNIT

SHUNT REGULATOR

STORAGE BATTERIES CHARGE REGULATOR

TO LOADS

Figure 3.2: The solar array is connected directly to the distribution unit in a DET system. A regulated DET system is achieved by replacing the diode with a discharge regulator.

Battery charging is dealt with by a dedicated charge regulator that charges the batteries with a constant current during the sunlit portion of the orbit.

For the unregulated DET system shown in Figure 3.2, the batteries discharge through a rectifying diode during the eclipse period, clamping the bus to a diode drop below the battery voltage. A regulated counterpart is also widely used where a dedicated discharge regulator can step up/down the battery voltage to match the desired bus voltage.

3.2.2 Peak Power Transfer (PPT)

In the PPT approach, a regulator is placed in series between the solar array and the loads. By taking control of the operating point on the solar array’s I-V curve, the regulator tries to operate the solar array in such a way as to maximize the power output from it. This increases efficiency and simultaneously side-steps the potential thermal dissipation problems seen in DET

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systems. Such a regulator is often called a Maximum Power Point Tracking (MPPT) regulator, and it is used to both charge the batteries and supply the loads with power.

SOLAR ARRAY

POWER DISTRIBUTION

UNIT PEAK POWER

TRACKING REGULATOR

STORAGE BATTERIES

TO LOADS

Figure 3.3: A maximum power point tracking regulator, controlling the output of the solar array, can be used to supply power to the loads and for battery charging at the same time.

When the batteries are fully charged, the tracker electronically moves the operating point away (towards the open-circuit condition) from the maximum power point, and in the process it leaves the energy from the sun as heat in the solar array itself, instead of converting it to electrical energy. Since a large portion of the incoming solar energy already is left as heat in the 28%

efficient panels during normal operation, an additional few percent does not pose a thermal problem as far as the solar array is concerned. Contrast this to the DET systems, where the excessive energy is dissipated inside of the spacecraft, which may give rise to some of the thermal problems discussed in Section 3.6.4. Yet another benefit with the PPT system is that the battery is connected directly to the loads. This maximizes efficiency during the eclipse, which is when we need it.

Before looking closer at how such a PPT system works, some of the orbit constraints will be introduced. By introducing them here, they will serve to back up the decision to choose a PPT system over a DET system, and also provide the backdrop for the energy storage discussion that follows i Section 3.5.

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3.3 Orbital Considerations

Since the final orbit details for CubeSTAR are presently undefined, the orbit considered here will be a typical Low Earth Orbit (LEO) Cubesat orbit, with an altitude of 600 km and an inclination of 98^◦. To simplify further, only the ”minimum Sun” case (i.e., maximum eclipse), where the Sun-Earth vector lies in the orbit plane, will be considered here. For all but the Sun synchronous low earth orbits, the Sun will lie in the orbit plane twice a year, allowing us to calculate the orbital parameters based on a simple argument from geometry. The minimum Sun case also returns valuable information about the energy storage requirements, as it defines the minimum battery capacity needed.

Figure 3.4: Orbital altitude put in perspective; the expected CubeSTAR altitude will be somewhere in between that of the Hubble Space telescope and ISS. By comparison, the Earth’s atmosphere (in blue) reaches up to about 100km where the first 10km contain 75% of the planet’s air.

3.3.1 Orbit Period and the Eclipse

The orbital period,T, is derived from Newton’s formulation of Kepler’s third law, but that is a derivation we shall not pursue here. Rather, we will simply reproduce the result from [15]:

Electrical power system for the CubeSTAR nanosatellite